def test_convex_subproblem(subproblem):
delta = 1.151
s, case = solve_nd_trust_region_subproblem(subproblem['B'],
subproblem['g'], delta)
assert np.all(np.real(linalg.eig(subproblem['B'])[0]) > 0)
assert norm(s) < delta
assert case == 'posdef'
assert is_local_quad_min(s, subproblem['B'], subproblem['g'])
def test_convex_subproblem(subproblem):
delta = 1.151
s, case = solve_nd_trust_region_subproblem(subproblem['B'],
subproblem['g'], delta)
assert np.all(np.real(linalg.eig(subproblem['B'])[0]) > 0)
assert norm(s) < delta
assert case == 'posdef'
assert is_local_quad_min(s, subproblem['B'], subproblem['g'])
for alpha in [0, 0.5, -0.5]:
sc = solve_1d_trust_region_subproblem(subproblem['B'], subproblem['g'],
s, delta, alpha * s)[0]
assert sc + alpha == 1
def test_nonconvex_subproblem_eigvals(subproblem, minev):
subproblem['B'][0, 0] = -minev
delta = 1.0
s, case = solve_nd_trust_region_subproblem(subproblem['B'],
subproblem['g'], delta)
assert np.any(np.real(linalg.eig(subproblem['B'])[0]) < 0)
assert np.isclose(norm(s), delta, atol=1e-6, rtol=0)
assert is_bound_quad_min(s, subproblem['B'], subproblem['g'])
assert not is_bound_quad_min(-s, subproblem['B'], subproblem['g'])
for alpha in [0, 0.5, -0.5]:
sc = solve_1d_trust_region_subproblem(subproblem['B'], subproblem['g'],
s, delta, alpha * s)[0]
assert np.isclose(sc + alpha, 1)
def test_nonconvex_subproblem_eigvals(subproblem, minev):
subproblem['B'][0, 0] = -minev
delta = 1.0
s, case = solve_nd_trust_region_subproblem(subproblem['B'],
subproblem['g'], delta)
assert np.any(np.real(linalg.eig(subproblem['B'])[0]) < 0)
assert np.isclose(norm(s), delta, atol=1e-6, rtol=0)
assert is_bound_quad_min(s, subproblem['B'], subproblem['g'])
snorm = s.copy()
normalize(snorm)
for alpha in [0, 0.5, -0.5]:
assert np.isclose(solve_1d_trust_region_subproblem(
subproblem['B'], subproblem['g'], snorm, delta, alpha * s
)[0], (1 - alpha)*delta)
def test_hard_hard_subproblem(subproblem):
subproblem['B'][0, 0] = -1.0
subproblem['g'][0] = 0.0
delta = 0.5
s, case = solve_nd_trust_region_subproblem(subproblem['B'],
subproblem['g'], delta)
assert np.any(np.real(linalg.eig(subproblem['B'])[0]) < 0)
assert np.isclose(norm(s), delta, atol=1e-6, rtol=0)
assert case == 'hard'
assert is_bound_quad_min(s, subproblem['B'], subproblem['g'])
snorm = s.copy()
normalize(snorm)
for alpha in [0, 0.5, -0.5]:
assert np.isclose(solve_1d_trust_region_subproblem(
subproblem['B'], subproblem['g'], snorm, delta, alpha * s
)[0], (1 - alpha)*delta)